I didn't name this proposal: 1. Determine defeats a la Symmetrical ICT
2. Discard defeats that are in cycles 3. If exactly one candidate is unbeaten, s/he wins 4. If all or no candidates are unbeaten, elect the most top-ranked 5. If some, but not all, candidates are unbeaten, elect the most top-ranked unbeaten candidate. ------------------------------------------------------------------------ I'll call it NC Symmetrical ICT (NC stands for "no cycles") ------------------------------------------------------------------------ It reminds me of something that I proposed a long time ago, which I called the "subcycle rule": Others have independently later proposed it. It seems to me that it turned out to have some problem that made it not a good idea. Whatever the method is, to "replace a cycle" means to apply the method to the members of that cycle, and replace the cycle with the winner. Replace every cycle that doesn't contain,as an element, a smaller cycle. Repeat till there are no cycles. ------------------------------------------------------------------------ Every rank method that I've proposed after Symmetrical ICT is proposed tentatively. Let me tentatively propose this: CR Symmetrical ICT. Determine defeats according to Symmetrical ICT. Do cycle replacement, as defined above, with Symmetrical ICT as the method. Apply Symmetrical ICT to the remaining candidates.. ------------------------------------------------------------------------ I don't know which, if any, of Symmetrical IC-Schwartz-Top, NC Symmetrical ICT, CR Symmetrical ICT, Symmetrical iC-Beatpath(lv), or Symmetrical IC-Rankded-Pairs(lv) are any good. My favorite of those is Symmetrical IC-Schwartz-Top, but I'm not sure. ---------------------------------------------------------------------------- For polling, the Condorcet Criterion might be desirable. If it's desired to do the best toward finding the CW, by encouraging complete sincere rankings, then ordinary ICT would be better than Symmetrical ICT, though no rank method really would encourage sincere rankings, for reasons that differ between methods. But if there are lots of candidates, and people wouldn't want to rank them all, and it's desired to not discourage voting, then Symmetrical ICT would be better, with an assurance that there's no need to rank unacceptable candidates. ------------------------------------------------------------------------- But suppose that people insisted on a ranked-method for official public elections? Maybe someday people will be interested in doing the very laborious handcounts needed by the rank methods, and dedicated enough to democracy to be willing to do that work. Maybe rank-method handcounting will be regarded as a good, socially productive source of lots of employment. In official public elections, it would be best to be able to assure people that they needn't rank unacceptables,and so Symmetrical ICT would be better than ICT. MMC would be desirable, whether for official elections or for polling. Methods such as Symmetrical IC-Schwartz-Top (if they don't have a problem that I don't know of) would gain it at the cost of trading FBC for 0-info non-top FBC (Weak FBC). AOCBucklin would get it by trading the Condorcet Criterion for it. Because I don't consider CC important in public elections, compared to the other criteria that I advocate, then that could be a good trade. But in order to get MMC, while keeping full FBC, comes at the cost of having defection-resistance that isn't quite as good as that of the ICT methods. An advantage of AOCBucklin for public elections is that it can be offered as an option in an Approval election. An option would be easier to propose and enact than a new method. There's something appealing about giving people a choice, in an election, between methods as diverse (though related) as Approval and AOCBucklin. A disadvantage of AOCBucklin is that the AOC part of it can't really be defined without a computer program. And the program-section that gives it the delay that confers MMC compliance greatly increases the length and complexity of its computer program--not that the count would be done by computer, because computer counting will probably never be fraud-secure. I don't know which of those methods' criterion and properties combinations would be best. It would depend on the desirability of FBC vs Weak FBC, compared to the desirability of ICT's better defection-resistance vs that of AOCBucklin, and the desirability of MMC vs Condorcet. As for the latter, MMC is almost surely more desirable in official public elections, as compared to CC. But, other than ICT, Symmetrical ICT and AOCBucklin, I don't know if any of these rank methods that I've been proposing would have some prohibitive problem that I don't know about, or if they really meet the criteria that they seem to meet. If there's some reason why merely disregarding defeats that are in cycles, as opposed to choosing from the Schwartz set, wouldn't achieve MMC for ICT, then I don't know why not. But I'm not saying that there isn't. As for Clone-Independence, I realize that ICT's top-count spoils that. Isn't the possibility of cycles among the majority-preferred set of candidates the only reason why ICT doesn't meet MMC? Mike Ossipoff - ---- Election-Methods mailing list - see http://electorama.com/em for list info